TSTP Solution File: REL013-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : REL013-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 13:43:53 EDT 2023
% Result : Unsatisfiable 0.20s 0.57s
% Output : Proof 1.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : REL013-1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 23:24:11 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.57 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.57
% 0.20/0.57 % SZS status Unsatisfiable
% 0.20/0.57
% 1.76/0.59 % SZS output start Proof
% 1.76/0.59 Take the following subset of the input axioms:
% 1.93/0.59 fof(composition_associativity_5, axiom, ![A, B, C]: composition(A, composition(B, C))=composition(composition(A, B), C)).
% 1.93/0.59 fof(composition_distributivity_7, axiom, ![A2, B2, C2]: composition(join(A2, B2), C2)=join(composition(A2, C2), composition(B2, C2))).
% 1.93/0.59 fof(composition_identity_6, axiom, ![A2]: composition(A2, one)=A2).
% 1.93/0.59 fof(converse_additivity_9, axiom, ![A2, B2]: converse(join(A2, B2))=join(converse(A2), converse(B2))).
% 1.93/0.59 fof(converse_cancellativity_11, axiom, ![A2, B2]: join(composition(converse(A2), complement(composition(A2, B2))), complement(B2))=complement(B2)).
% 1.93/0.59 fof(converse_idempotence_8, axiom, ![A2]: converse(converse(A2))=A2).
% 1.93/0.60 fof(converse_multiplicativity_10, axiom, ![A2, B2]: converse(composition(A2, B2))=composition(converse(B2), converse(A2))).
% 1.93/0.60 fof(def_top_12, axiom, ![A2]: top=join(A2, complement(A2))).
% 1.93/0.60 fof(def_zero_13, axiom, ![A2]: zero=meet(A2, complement(A2))).
% 1.93/0.60 fof(goals_14, negated_conjecture, composition(sk1, zero)!=zero | composition(zero, sk1)!=zero).
% 1.93/0.60 fof(maddux1_join_commutativity_1, axiom, ![A2, B2]: join(A2, B2)=join(B2, A2)).
% 1.93/0.60 fof(maddux2_join_associativity_2, axiom, ![A2, B2, C2]: join(A2, join(B2, C2))=join(join(A2, B2), C2)).
% 1.93/0.60 fof(maddux3_a_kind_of_de_Morgan_3, axiom, ![A2, B2]: A2=join(complement(join(complement(A2), complement(B2))), complement(join(complement(A2), B2)))).
% 1.93/0.60 fof(maddux4_definiton_of_meet_4, axiom, ![A2, B2]: meet(A2, B2)=complement(join(complement(A2), complement(B2)))).
% 1.93/0.60
% 1.93/0.60 Now clausify the problem and encode Horn clauses using encoding 3 of
% 1.93/0.60 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 1.93/0.60 We repeatedly replace C & s=t => u=v by the two clauses:
% 1.93/0.60 fresh(y, y, x1...xn) = u
% 1.93/0.60 C => fresh(s, t, x1...xn) = v
% 1.93/0.60 where fresh is a fresh function symbol and x1..xn are the free
% 1.93/0.60 variables of u and v.
% 1.93/0.60 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 1.93/0.60 input problem has no model of domain size 1).
% 1.93/0.60
% 1.93/0.60 The encoding turns the above axioms into the following unit equations and goals:
% 1.93/0.60
% 1.93/0.60 Axiom 1 (composition_identity_6): composition(X, one) = X.
% 1.93/0.60 Axiom 2 (maddux1_join_commutativity_1): join(X, Y) = join(Y, X).
% 1.93/0.60 Axiom 3 (converse_idempotence_8): converse(converse(X)) = X.
% 1.93/0.60 Axiom 4 (def_top_12): top = join(X, complement(X)).
% 1.93/0.60 Axiom 5 (def_zero_13): zero = meet(X, complement(X)).
% 1.93/0.60 Axiom 6 (converse_multiplicativity_10): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 1.93/0.60 Axiom 7 (composition_associativity_5): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 1.93/0.60 Axiom 8 (converse_additivity_9): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 1.93/0.60 Axiom 9 (maddux2_join_associativity_2): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 1.93/0.60 Axiom 10 (maddux4_definiton_of_meet_4): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 1.93/0.60 Axiom 11 (composition_distributivity_7): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 1.93/0.60 Axiom 12 (converse_cancellativity_11): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 1.93/0.60 Axiom 13 (maddux3_a_kind_of_de_Morgan_3): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 1.93/0.60
% 1.93/0.60 Lemma 14: complement(top) = zero.
% 1.93/0.60 Proof:
% 1.93/0.60 complement(top)
% 1.93/0.60 = { by axiom 4 (def_top_12) }
% 1.93/0.60 complement(join(complement(X), complement(complement(X))))
% 1.93/0.60 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 1.93/0.60 meet(X, complement(X))
% 1.93/0.60 = { by axiom 5 (def_zero_13) R->L }
% 1.93/0.60 zero
% 1.93/0.60
% 1.93/0.60 Lemma 15: composition(converse(one), X) = X.
% 1.93/0.60 Proof:
% 1.93/0.60 composition(converse(one), X)
% 1.93/0.60 = { by axiom 3 (converse_idempotence_8) R->L }
% 1.93/0.60 composition(converse(one), converse(converse(X)))
% 1.93/0.60 = { by axiom 6 (converse_multiplicativity_10) R->L }
% 1.93/0.60 converse(composition(converse(X), one))
% 1.93/0.60 = { by axiom 1 (composition_identity_6) }
% 1.93/0.60 converse(converse(X))
% 1.93/0.60 = { by axiom 3 (converse_idempotence_8) }
% 1.93/0.60 X
% 1.93/0.60
% 1.93/0.60 Lemma 16: converse(one) = one.
% 1.93/0.60 Proof:
% 1.93/0.60 converse(one)
% 1.93/0.60 = { by axiom 1 (composition_identity_6) R->L }
% 1.93/0.60 composition(converse(one), one)
% 1.93/0.60 = { by lemma 15 }
% 1.93/0.60 one
% 1.93/0.60
% 1.93/0.60 Lemma 17: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 1.93/0.60 Proof:
% 1.93/0.60 join(meet(X, Y), complement(join(complement(X), Y)))
% 1.93/0.60 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 1.93/0.60 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 1.93/0.60 = { by axiom 13 (maddux3_a_kind_of_de_Morgan_3) R->L }
% 1.93/0.60 X
% 1.93/0.60
% 1.93/0.60 Lemma 18: composition(one, X) = X.
% 1.93/0.60 Proof:
% 1.93/0.60 composition(one, X)
% 1.93/0.60 = { by lemma 15 R->L }
% 1.93/0.60 composition(converse(one), composition(one, X))
% 1.93/0.60 = { by axiom 7 (composition_associativity_5) }
% 1.93/0.60 composition(composition(converse(one), one), X)
% 1.93/0.60 = { by axiom 1 (composition_identity_6) }
% 1.93/0.60 composition(converse(one), X)
% 1.93/0.60 = { by lemma 15 }
% 1.93/0.60 X
% 1.93/0.60
% 1.93/0.60 Lemma 19: join(complement(X), composition(converse(Y), complement(composition(Y, X)))) = complement(X).
% 1.93/0.60 Proof:
% 1.93/0.60 join(complement(X), composition(converse(Y), complement(composition(Y, X))))
% 1.93/0.60 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 1.93/0.60 join(composition(converse(Y), complement(composition(Y, X))), complement(X))
% 1.93/0.60 = { by axiom 12 (converse_cancellativity_11) }
% 1.93/0.60 complement(X)
% 1.93/0.60
% 1.93/0.60 Lemma 20: join(complement(X), complement(X)) = complement(X).
% 1.93/0.60 Proof:
% 1.93/0.60 join(complement(X), complement(X))
% 1.93/0.60 = { by lemma 15 R->L }
% 1.93/0.60 join(complement(X), composition(converse(one), complement(X)))
% 1.93/0.60 = { by lemma 18 R->L }
% 1.93/0.60 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 1.93/0.60 = { by lemma 19 }
% 1.93/0.60 complement(X)
% 1.93/0.60
% 1.93/0.60 Lemma 21: join(zero, zero) = zero.
% 1.93/0.60 Proof:
% 1.93/0.60 join(zero, zero)
% 1.93/0.60 = { by lemma 14 R->L }
% 1.93/0.60 join(zero, complement(top))
% 1.93/0.60 = { by lemma 14 R->L }
% 1.93/0.60 join(complement(top), complement(top))
% 1.93/0.60 = { by lemma 20 }
% 1.93/0.60 complement(top)
% 1.93/0.60 = { by lemma 14 }
% 1.93/0.60 zero
% 1.93/0.60
% 1.93/0.60 Lemma 22: join(zero, join(zero, X)) = join(X, zero).
% 1.93/0.60 Proof:
% 1.93/0.60 join(zero, join(zero, X))
% 1.93/0.60 = { by axiom 9 (maddux2_join_associativity_2) }
% 1.93/0.60 join(join(zero, zero), X)
% 1.93/0.60 = { by lemma 21 }
% 1.93/0.60 join(zero, X)
% 1.93/0.60 = { by axiom 2 (maddux1_join_commutativity_1) }
% 1.93/0.60 join(X, zero)
% 1.93/0.60
% 1.93/0.60 Lemma 23: join(X, zero) = X.
% 1.93/0.60 Proof:
% 1.93/0.60 join(X, zero)
% 1.93/0.60 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 1.93/0.60 join(zero, X)
% 1.93/0.60 = { by lemma 17 R->L }
% 1.93/0.60 join(zero, join(meet(X, complement(X)), complement(join(complement(X), complement(X)))))
% 1.93/0.60 = { by axiom 5 (def_zero_13) R->L }
% 1.93/0.60 join(zero, join(zero, complement(join(complement(X), complement(X)))))
% 1.93/0.60 = { by axiom 10 (maddux4_definiton_of_meet_4) R->L }
% 1.93/0.60 join(zero, join(zero, meet(X, X)))
% 1.93/0.60 = { by lemma 22 }
% 1.93/0.60 join(meet(X, X), zero)
% 1.93/0.60 = { by axiom 10 (maddux4_definiton_of_meet_4) }
% 1.93/0.60 join(complement(join(complement(X), complement(X))), zero)
% 1.93/0.60 = { by lemma 20 }
% 1.93/0.60 join(complement(complement(X)), zero)
% 1.93/0.60 = { by axiom 2 (maddux1_join_commutativity_1) }
% 1.93/0.60 join(zero, complement(complement(X)))
% 1.93/0.60 = { by axiom 5 (def_zero_13) }
% 1.93/0.60 join(meet(X, complement(X)), complement(complement(X)))
% 1.93/0.60 = { by lemma 20 R->L }
% 1.93/0.60 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 1.93/0.60 = { by lemma 17 }
% 1.93/0.60 X
% 1.93/0.60
% 1.93/0.60 Lemma 24: converse(join(X, converse(Y))) = join(Y, converse(X)).
% 1.93/0.60 Proof:
% 1.93/0.60 converse(join(X, converse(Y)))
% 1.93/0.60 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 1.93/0.60 converse(join(converse(Y), X))
% 1.93/0.60 = { by axiom 8 (converse_additivity_9) }
% 1.93/0.60 join(converse(converse(Y)), converse(X))
% 1.93/0.60 = { by axiom 3 (converse_idempotence_8) }
% 1.93/0.60 join(Y, converse(X))
% 1.93/0.60
% 1.93/0.60 Lemma 25: converse(join(converse(X), Y)) = join(X, converse(Y)).
% 1.93/0.60 Proof:
% 1.93/0.60 converse(join(converse(X), Y))
% 1.93/0.60 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 1.93/0.60 converse(join(Y, converse(X)))
% 1.93/0.60 = { by lemma 24 }
% 1.93/0.60 join(X, converse(Y))
% 1.93/0.60
% 1.93/0.60 Lemma 26: converse(zero) = zero.
% 1.93/0.60 Proof:
% 1.93/0.60 converse(zero)
% 1.93/0.60 = { by lemma 23 R->L }
% 1.93/0.60 join(converse(zero), zero)
% 1.93/0.60 = { by lemma 22 R->L }
% 1.93/0.60 join(zero, join(zero, converse(zero)))
% 1.93/0.60 = { by lemma 25 R->L }
% 1.93/0.60 join(zero, converse(join(converse(zero), zero)))
% 1.93/0.60 = { by lemma 23 }
% 1.93/0.60 join(zero, converse(converse(zero)))
% 1.93/0.60 = { by axiom 3 (converse_idempotence_8) }
% 1.93/0.60 join(zero, zero)
% 1.93/0.60 = { by lemma 21 }
% 1.93/0.60 zero
% 1.93/0.60
% 1.93/0.60 Lemma 27: join(X, join(Y, complement(X))) = join(Y, top).
% 1.93/0.60 Proof:
% 1.93/0.60 join(X, join(Y, complement(X)))
% 1.93/0.60 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 1.93/0.60 join(X, join(complement(X), Y))
% 1.93/0.60 = { by axiom 9 (maddux2_join_associativity_2) }
% 1.93/0.60 join(join(X, complement(X)), Y)
% 1.93/0.60 = { by axiom 4 (def_top_12) R->L }
% 1.93/0.60 join(top, Y)
% 1.93/0.60 = { by axiom 2 (maddux1_join_commutativity_1) }
% 1.93/0.60 join(Y, top)
% 1.93/0.60
% 1.93/0.60 Lemma 28: join(top, complement(X)) = top.
% 1.93/0.60 Proof:
% 1.93/0.60 join(top, complement(X))
% 1.93/0.60 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 1.93/0.60 join(complement(X), top)
% 1.93/0.60 = { by lemma 27 R->L }
% 1.93/0.60 join(X, join(complement(X), complement(X)))
% 1.93/0.60 = { by lemma 20 }
% 1.93/0.60 join(X, complement(X))
% 1.93/0.60 = { by axiom 4 (def_top_12) R->L }
% 1.93/0.60 top
% 1.93/0.60
% 1.93/0.60 Lemma 29: join(zero, X) = X.
% 1.93/0.60 Proof:
% 1.93/0.60 join(zero, X)
% 1.93/0.60 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 1.93/0.60 join(X, zero)
% 1.93/0.60 = { by lemma 23 }
% 1.93/0.60 X
% 1.93/0.60
% 1.93/0.60 Lemma 30: join(top, X) = top.
% 1.93/0.60 Proof:
% 1.93/0.60 join(top, X)
% 1.93/0.60 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 1.93/0.60 join(X, top)
% 1.93/0.60 = { by lemma 28 R->L }
% 1.93/0.60 join(X, join(top, complement(X)))
% 1.93/0.60 = { by lemma 27 }
% 1.93/0.60 join(top, top)
% 1.93/0.60 = { by lemma 27 R->L }
% 1.93/0.60 join(zero, join(top, complement(zero)))
% 1.93/0.60 = { by lemma 28 }
% 1.93/0.60 join(zero, top)
% 1.93/0.60 = { by lemma 29 }
% 1.93/0.60 top
% 1.93/0.60
% 1.93/0.60 Lemma 31: join(X, composition(Y, X)) = composition(join(Y, one), X).
% 1.93/0.60 Proof:
% 1.93/0.60 join(X, composition(Y, X))
% 1.93/0.60 = { by lemma 18 R->L }
% 1.93/0.60 join(composition(one, X), composition(Y, X))
% 1.93/0.60 = { by axiom 11 (composition_distributivity_7) R->L }
% 1.93/0.60 composition(join(one, Y), X)
% 1.93/0.60 = { by axiom 2 (maddux1_join_commutativity_1) }
% 1.93/0.60 composition(join(Y, one), X)
% 1.93/0.60
% 1.93/0.60 Lemma 32: composition(X, join(one, one)) = join(X, X).
% 1.93/0.60 Proof:
% 1.93/0.60 composition(X, join(one, one))
% 1.93/0.61 = { by lemma 16 R->L }
% 1.93/0.61 composition(X, join(one, converse(one)))
% 1.93/0.61 = { by lemma 16 R->L }
% 1.93/0.61 composition(X, join(converse(one), converse(one)))
% 1.93/0.61 = { by axiom 8 (converse_additivity_9) R->L }
% 1.93/0.61 composition(X, converse(join(one, one)))
% 1.93/0.61 = { by axiom 3 (converse_idempotence_8) R->L }
% 1.93/0.61 composition(converse(converse(X)), converse(join(one, one)))
% 1.93/0.61 = { by axiom 6 (converse_multiplicativity_10) R->L }
% 1.93/0.61 converse(composition(join(one, one), converse(X)))
% 1.93/0.61 = { by lemma 16 R->L }
% 1.93/0.61 converse(composition(join(converse(one), one), converse(X)))
% 1.93/0.61 = { by lemma 31 R->L }
% 1.93/0.61 converse(join(converse(X), composition(converse(one), converse(X))))
% 1.93/0.61 = { by lemma 15 }
% 1.93/0.61 converse(join(converse(X), converse(X)))
% 1.93/0.61 = { by lemma 25 }
% 1.93/0.61 join(X, converse(converse(X)))
% 1.93/0.61 = { by axiom 3 (converse_idempotence_8) }
% 1.93/0.61 join(X, X)
% 1.93/0.61
% 1.93/0.61 Lemma 33: join(composition(X, zero), composition(X, zero)) = composition(X, zero).
% 1.93/0.61 Proof:
% 1.93/0.61 join(composition(X, zero), composition(X, zero))
% 1.93/0.61 = { by lemma 32 R->L }
% 1.93/0.61 composition(composition(X, zero), join(one, one))
% 1.93/0.61 = { by axiom 7 (composition_associativity_5) R->L }
% 1.93/0.61 composition(X, composition(zero, join(one, one)))
% 1.93/0.61 = { by lemma 32 }
% 1.93/0.61 composition(X, join(zero, zero))
% 1.93/0.61 = { by lemma 21 }
% 1.93/0.61 composition(X, zero)
% 1.93/0.61
% 1.93/0.61 Lemma 34: composition(top, zero) = zero.
% 1.93/0.61 Proof:
% 1.93/0.61 composition(top, zero)
% 1.93/0.61 = { by lemma 14 R->L }
% 1.93/0.61 composition(top, complement(top))
% 1.93/0.61 = { by lemma 30 R->L }
% 1.93/0.61 composition(join(top, one), complement(top))
% 1.93/0.61 = { by lemma 30 R->L }
% 1.93/0.61 composition(join(join(top, converse(top)), one), complement(top))
% 1.93/0.61 = { by lemma 24 R->L }
% 1.93/0.61 composition(join(converse(join(top, converse(top))), one), complement(top))
% 1.93/0.61 = { by lemma 30 }
% 1.93/0.61 composition(join(converse(top), one), complement(top))
% 1.93/0.61 = { by lemma 31 R->L }
% 1.93/0.61 join(complement(top), composition(converse(top), complement(top)))
% 1.93/0.61 = { by lemma 30 R->L }
% 1.93/0.61 join(complement(top), composition(converse(top), complement(join(top, composition(top, top)))))
% 1.93/0.61 = { by lemma 31 }
% 1.93/0.61 join(complement(top), composition(converse(top), complement(composition(join(top, one), top))))
% 1.93/0.61 = { by lemma 30 }
% 1.93/0.61 join(complement(top), composition(converse(top), complement(composition(top, top))))
% 1.93/0.61 = { by lemma 19 }
% 1.93/0.61 complement(top)
% 1.93/0.61 = { by lemma 14 }
% 1.93/0.61 zero
% 1.93/0.61
% 1.93/0.61 Lemma 35: composition(X, zero) = zero.
% 1.93/0.61 Proof:
% 1.93/0.61 composition(X, zero)
% 1.93/0.61 = { by lemma 33 R->L }
% 1.93/0.61 join(composition(X, zero), composition(X, zero))
% 1.93/0.61 = { by lemma 29 R->L }
% 1.93/0.61 join(composition(X, zero), join(zero, composition(X, zero)))
% 1.93/0.61 = { by axiom 2 (maddux1_join_commutativity_1) R->L }
% 1.93/0.61 join(composition(X, zero), join(composition(X, zero), zero))
% 1.93/0.61 = { by axiom 9 (maddux2_join_associativity_2) }
% 1.93/0.61 join(join(composition(X, zero), composition(X, zero)), zero)
% 1.93/0.61 = { by lemma 33 }
% 1.93/0.61 join(composition(X, zero), zero)
% 1.93/0.61 = { by lemma 34 R->L }
% 1.93/0.61 join(composition(X, zero), composition(top, zero))
% 1.93/0.61 = { by axiom 11 (composition_distributivity_7) R->L }
% 1.93/0.61 composition(join(X, top), zero)
% 1.93/0.61 = { by axiom 2 (maddux1_join_commutativity_1) }
% 1.93/0.61 composition(join(top, X), zero)
% 1.93/0.61 = { by lemma 30 }
% 1.93/0.61 composition(top, zero)
% 1.93/0.61 = { by lemma 34 }
% 1.93/0.61 zero
% 1.93/0.61
% 1.93/0.61 Goal 1 (goals_14): tuple(composition(zero, sk1), composition(sk1, zero)) = tuple(zero, zero).
% 1.93/0.61 Proof:
% 1.93/0.61 tuple(composition(zero, sk1), composition(sk1, zero))
% 1.93/0.61 = { by axiom 3 (converse_idempotence_8) R->L }
% 1.93/0.61 tuple(converse(converse(composition(zero, sk1))), composition(sk1, zero))
% 1.93/0.61 = { by axiom 6 (converse_multiplicativity_10) }
% 1.93/0.61 tuple(converse(composition(converse(sk1), converse(zero))), composition(sk1, zero))
% 1.93/0.61 = { by lemma 26 }
% 1.93/0.61 tuple(converse(composition(converse(sk1), zero)), composition(sk1, zero))
% 1.93/0.61 = { by lemma 35 }
% 1.93/0.61 tuple(converse(zero), composition(sk1, zero))
% 1.93/0.61 = { by lemma 26 }
% 1.93/0.61 tuple(zero, composition(sk1, zero))
% 1.93/0.61 = { by lemma 35 }
% 1.93/0.61 tuple(zero, zero)
% 1.93/0.61 % SZS output end Proof
% 1.93/0.61
% 1.93/0.61 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------